On simple $n$-tuples of subspaces of a Hilbert space
This survey is devoted to the structure of “simple” systems $S = (H;H_1,…,H_n)$ of subspaces $H_i,\; i = 1,…, n,$ of a Hilbert space $H$, i.e., $n$-tuples of subspaces such that, for each pair of subspaces $H_i$ and $H_j$, the angle $0 < θ_{ij} ≤ π/2$ between them is fixed. We give a descript...
Gespeichert in:
| Datum: | 2009 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2009
|
| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3130 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | This survey is devoted to the structure of “simple” systems $S = (H;H_1,…,H_n)$ of subspaces $H_i,\; i = 1,…, n,$ of a Hilbert space $H$, i.e., $n$-tuples of subspaces such that, for each pair of subspaces $H_i$ and $H_j$, the angle $0 < θ_{ij} ≤ π/2$ between them is fixed. We give a description of “simple” systems of subspaces in the case where the labeled graphs naturally associated with these systems are trees or unicyclic graphs and also in the case where all subspaces are one-dimensional. If the cyclic range of a graph is greater than or equal to two, then the problem of description of all systems of this type up to unitary equivalence is *-wild. |
|---|